Adamaszek, Anna, Czumaj, Artur and Lingas, Andrzej. (2010) PTAS for k-tour cover problem on the plane for moderately large values of k. International Journal of Foundations of Computer Science, Vol.21 (No.6). pp. 893-904. ISSN 0129-0541

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Abstract

Let P be a set of n points in the Euclidean plane and let O be the origin point in the plane. In the k-tour cover problem (called frequently the capacitated vehicle routing problem), the goal is to minimize the total length of tours that cover all points in P, such that each tour starts and ends in O and covers at most k points from P. The k-tour cover problem is known to be NP-hard. It is also known to admit constant factor approximation algorithms for all values of k and even a polynomial-time approximation scheme (PTAS) for small values of k, k = circle divide (log n/ log log n). In this paper, we significantly enlarge the set of values of k for which a PTAS is provable. We present a new PTAS for all values of k <= 2(log delta n), where delta = delta(epsilon). The main technical result proved in the paper is a novel reduction of the k-tour cover problem with a set of n points to a small set of instances of the problem, each with circle divide((k/epsilon)(circle divide(1))) points.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software
Divisions:	Faculty of Science > Computer Science
Journal or Publication Title:	International Journal of Foundations of Computer Science
Publisher:	World Scientific Publishing Co. Pte. Ltd.
ISSN:	0129-0541
Date:	December 2010
Volume:	Vol.21
Number:	No.6
Page Range:	pp. 893-904
Identification Number:	10.1142/S0129054110007623
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
URI:	http://wrap.warwick.ac.uk/id/eprint/41591

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